arXiv
Open Access
2026
Irrational series II Summation by packages
Olivier Thom
Abstrak
Discrete sums of exponentials $g(w) = \sum a_β \mathrm{e}^{βw}$ with positive exponents may converge not normally in neighborhoods $H$ of $-\infty$ which do not contain half-planes. We study different notions of convergence for these series and in particular the intuitive notion of summation by packages. Indeed, joining in packages the terms in the sum $g(w)$ whose exponents are close together, and summing first inside each package may result in massive cancellations. We show that discrete sums $g(w)$ which are bounded in what we call logarithmic neighborhoods can always be summated by packages.
Topik & Kata Kunci
Penulis (1)
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Olivier Thom
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2026
- Bahasa
- en
- Sumber Database
- arXiv
- Akses
- Open Access ✓